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Chapter 8
Competitive Firms
and Markets
The love of money is the root of all
virtue.
George Bernard Shaw
Chapter 8 Outline
Challenge: The Rising Cost of Keeping on Truckin’
8.1 Perfect Competition
8.2 Profit Maximization
8.3 Competition in the Short Run
8.4 Competition in the Long Run
Challenge Solution
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8-2
Challenge: The Rising Cost
of Keeping on Truckin’
• Background:
• In recent years, federal and state fees have increased
substantially and truckers have had to adhere to many
new regulations.
• The many additional fees and costly regulations that a
trucker or firm must pay to operate are largely lump-sum
costs, which are not related to the number of miles driven.
• Questions:
• What effect do these new fixed costs have on the trucking
industry’s market price and quantity?
• Are individual firms providing more or fewer trucking
services?
• Does the number of firms in the market rise or fall?
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8-3
8.1 Perfect Competition
• Market structure provides information about how firms
operating in the market will behave; it is a function of:
• the number of firms in the market
• the ease with which firms can enter and leave the market
• the ability of firms to differentiate their products from those
of their rivals
• Perfect competition is one type of market structure in
which buyers and sellers choose to be price takers.
• A firm is unable to sell its output at a price greater than
market price. A consumer is unable to purchase at a price
less than the market price.
• This is what most people mean when they talk about
“competitive firms,”, “competitive sellers,” and “competitive
buyers,”,
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8-4
8.1 Perfect Competition
• Perfect competition is a market structure in which:
• there are a large number of firms
• firms sell identical products
• buyers and sellers have full information about prices
charged by all firms
• transaction costs, the expenses of finding a trading
partner and completing the trade above and beyond
the price, are low
• firms can freely enter and exit the market
• Examples:
• Agricultural/commodities markets like wheat and
soybeans
• Building and construction
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8-5
8.1 Perfect Competition:
Assumptions
1. Large number of firms
•
•
No single firm’s actions can raise or lower the price.
Individual firm’s demand curve is a horizontal line at market price.
2. Identical (homogeneous) products
•
If all firms are selling identical products, it is difficult for any firm to
raise the price above the going market price charged by all firms.
3. Full information
•
Consumer knowledge of all firms’ prices makes it easy for consumers to
buy elsewhere if any one firm raised its price above market price.
4. Negligible transaction costs
•
Buyers and sellers waste little time or money finding each other.
5. Free entry and exit
•
Leads to large number of firms and promotes price taking.
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8-6
8.1 Competitive Firm’s Demand
• Are perfectly competitive firms’ demand curves really
flat?
– P(q)=p where p is exogenous market price
– A competitive firm is a price taker
• A firm’s residual demand curve, Dr(p), is the portion
of the market demand that is not met by other sellers
at any given price.
• D(p) = market demand
• So(p) = amount supplied by other firms
• If not perfectly horizontal, the residual demand curve of
an individual firm is much flatter than market demand.
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8-7
8.1 Competitive Firm’s Demand
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8-8
8.1 Competitive Firm’s Demand
•
•
•
•
Elasticity of residual demand
By taking derivative w.r.t. p of Dr(p)
Dr(p)/dp = D(p) /dp − So(p) /dp.
Multiplying both sides by p/q and adjustment terms
where q=Dr(p), Q=D(p) & QO= So(p).
• [Dr(p)/dp][p/q] = [D(p) /dp] [p/Q] [Q/q] − [So(p) /dp]
[p/QO][QO/q]
• εi=nε-(n-1)ηO
• Implication of horizontal individual demand
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8-9
8.2 Profit Maximization
• Profit maximization in this class always refers to
economic profit, which is revenue minus opportunity
cost. π(q) = R(q) − C(q).
• Differs from business profit, which only subtracts off
explicit costs from revenues.
• Maximizing profit involves two important questions:
1.Output decision: If the firm produces, what output
level (q*) maximizes its profit or minimizes its loss?
2.Shutdown decision: Is it more profitable to produce
q* or to shut down and produce no output?
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8-10
8.2 Profit Maximization: Output
Rules
• Max{q} π(q) = R(q) − C(q).
• A firm can use one of three equivalent output
rules to choose how much output to produce:
1. A firm sets its output where its profit is
maximized.
2. A firm sets its output where its marginal profit is
zero.
3. A firm sets its output where its marginal revenue
equals its marginal cost.
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8-11
8.2 Profit Maximization: Output
Rules
• Output rule #3 (marginal revenue = marginal
cost) is less obvious on the previous graph.
• Mathematically, if we take the derivative of
π(q) = R(q) – C(q) with respect to output and
set it equal to zero (output rule #2), we find:
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8-12
8.2 Profit Maximization: Shutdown
Rule
• A firm shuts down only if it can reduce its loss by doing
so.
• Shutting down means that the firm stops producing
(and thus stops receiving revenue) and stops paying
avoidable costs. q=0 so that TR(0)=0.
• Only fixed costs are unavoidable because they are sunk
costs. C(0)=FC so that π (0)=-FC.
• Firms compare revenue to variable cost when deciding
whether to stop operating.
• Shutting down may be temporary.
• The shut down decision is a short run decision because,
in the long run all costs are avoidable.
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8-13
8.3 Competition in the Short Run
• Given this general description of firms’ profit
maximization decisions, how do perfectly competitive
firms maximize profits in the SR?
• Because it faces a horizontal demand curve, a
competitive firm can sell as many units of output as it
wants at the market price, p.
• Revenue is R(q) = pq, thus, q* satisfies:
• Marginal cost equals the market price
• MC = p is equivalent to MC = MR because MR = p in
perfect competition.
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8-14
8.3 Competition in the Short Run
• Output rules #1 (maximum profit) at q*
R(q)=pq
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8-15
8.3 Competition in the Short Run
• Output rules #1 (maximum profit) and #2
(zero marginal profit) both point to q*.
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8-16
8.3 Competition in the Short Run
R(q)=pq
p=MR>MC
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p=MR<MC
8-17
8.3 Competition in the Short Run
• Profit is the rectangle q*(p-AC(q*))
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8-18
8.3 Competition in the Short Run
C(q)
R(q)=pq
Loss>Fixed cost
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8-19
8.3 Competition in the Short Run
• Firms suffer loss greater than FC if operating revenue is
smaller than corresponding variable costs:
• Shut down if market price is less than the minimum of
its SR average variable cost curve.
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8-20
8.3 The Short-Run Shutdown
Decision
• If AC(q*)>p>AVC(q*), then firm operates, but at a loss.
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8-21
8.3 The Short-Run Shutdown
Decision
• If AVC(q)>p, then firm will shut down.
p
Additional loss beyond FC if operating at p=MC
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8-22
8.3 Short-Run Firm Supply Curve
• Firms will choose to produce as long as market price is
above the AVC minimum, so that is where a firm’s
supply curve begins.
• As we consider higher and higher market prices, the
horizontal firm demand curve rises and intersects MC at
higher and higher quantities.
• In this fashion, the relationship between market price
and profit-maximizing quantity is traced out.
• This is the perfectly competitive firm’s supply curve.
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8-23
8.3 Short-Run Firm Supply Curve
• S is the section of MC above min AVC.
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8-24
EX1: c(q)=0.0003q3-0.24q2+70q+3000
AC=0.0003q2-0.24q+70+3000/q
FC=3000
AVC=0.0003q2-0.24q+70
MC=0.0009q2-0.48q+70
AVC=MC at q=400 where AVC=MC=22
AC=MC at q≈427 where AC=MC≈29.24
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8-25
EX1: c(q)=0.0003q3-0.24q2+70q+3000
• Let q* be where P=MC
• If P≥29.24, MC>AC at q* π(q*)>0
– If P=50, P=MC when q≒489 or 46 (where MC is decreasing in q). So
q*=489, π≒9530
• If 29.24≥P≥22, AC>MC>AVC at q*  -FC<π(q*)<0
– If P=25, P=MC when q≒412 or 121 (where MC is decreasing in q). So
q*=412, π≒-1782>-3000
• If P≤22, AVC>MC at q* π<-FC at q* where P=MC, the
firm is better off shutting down
– If P=22, where MC=AVA at q=400, TR(q=400)=8800,
TVC(q=400)=8800, π(q=400)=-FC=-3000
– If P=10, P=MC when q≒333 or 200 (where MC is decreasing in q). But
when q=333, π≒-7446<-3000
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8-26
8.3 Short-Run Firm Supply Curve
AC,
M
C,
P
29.24
MC
Individual Supply
AC
AVC
22
400 427
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q
8-27
8.3 Short-Run Firm Supply Curve
• If the prices of inputs (factor prices) increase, a
firm’s production costs rise and its supply shifts left
(up).
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8-28
8.3 Short-Run Market Supply
(Identical Firms)
• The market supply curve is the horizontal sum
of the firm supply curves.
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8-29
8.3 Short-Run Market Supply
(Different Firms)
• The market supply curve is the horizontal sum of the
firm supply curves.
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8-30
Example 2: c(q)=q2+1
• TVC=q2, FC=1.
AVC=q<MC=2q
• The optimal q* is the
level of output where
MC(q*)=P
MC=2q*=P
→Si(p)=q*=P/2

P,MC
P2
MC
Individual
Supply Si(p)
P1
The individual supply is the
firm’s MC curve.
Industrial supply with n
identical firms is Q(P)=nP/2.

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q *1 q * 2 q
8-31
8.3 Short-Run Competitive
Equilibrium
• Market equilibrium (point E1) indicates price faced by
individual firm, and therefore, profit-maximizing
quantity, q1 with market demand D1.
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8-32
SR Market Equilibrium
• Suppose the industry Demand QD=100-P
• Individual short-run supply qi*=P/2
(c(qi)=qi2+1). Suppose n=8 (identical), the
short-run industrial supply QS=Σq=nP/2=4P
• The market is in SR competitive equilibrium
if QD=QS, such that 100-P=4P.
• The short-run eq. P=20. qi=10, Q=80.
• Every firm earns 200-101=99 in the shortrun.
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8-33
• Suppose the industry Demand changes to
QD=50-P (Why?)
• The market is in SR competitive equilibrium if
QD=QS, such that 50-P=4P.
• The short-run eq. becomes P=10. qi=5, Q=40.
• The demand decreases. As a result, each firm
produces less, equilibrium price drops, and the
aggregate output level shrinks. (Each makes a
smaller profit.)
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8-34
8.4 Competition in the Long Run
• Long-Run Output Decision
• The firm chooses the quantity that maximizes
profit using the same rule as in the SR: MC = MR.
• Long-Run Shutdown Decision
• Because all costs are variable in the LR, the firm
shuts down if it would suffer an economic loss by
continuing to operate.
• Graphically, relevant shutdown point is the
minimum of the LR average cost curve.
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8-35
8.4 Long-Run Firm Supply Curve
• Firm produces more
in the LR than in the
SR
• 110 units instead
of just 50 units
• Firm earns higher
profit in the LR than
in the SR.
• A+B instead of
just A
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8-36
• The long-run Individual supply is flatter than
the short-run individual supply for:
– LMC is flatter than SMC at any q.
– The firm has more flexibilities adjusting its scale
(K) so that marginal cost increases less as the
level of output increases or decreases more as
the level of output decreases from q.
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8-37
8.4 Long-Run Market Supply Curve
• As in the SR, the LR competitive market supply curve is
the horizontal sum of individual firm supply curves.
• In the LR, firms can enter or exit the market, so the
number of firms is not fixed as it is in the SR.
• A firm enters the market if it can make a long-run
profit.
• A firm exits the market to avoid a long-run loss.
• With identical firms, free entry into the market, and
constant input prices the LR market supply curve is flat
at the minimum LRAC.
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8-38
8.4 Long-Run Market Supply Curve
• Identical firms, free entry into the market, and
constant input prices.
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8-39
8.4 Long-Run Market Supply Curve
• Three scenarios in which LR market supply is not flat:
1.LR market supply when entry is limited
•
Upward-sloping if government restricts number of firms, firms
need a scarce resource, or if entry is costly
2.LR market supply when firms differ
•
Upward-sloping if firms with relatively low minimum LRAC are
willing to enter market at lower prices than others
3.LR market supply when input prices vary with output
•
•
In an increasing-cost market input prices rise with output
and LR market supply is upward-sloping
In a decreasing-cost market input prices fall with output
and LR market supply is downward-sloping
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8-40
8.4 Long-Run Market Supply Curve:
Increasing-Cost Market
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8-41
8.4 Long-Run Competitive
Equilibrium
• Equilibrium occurs at the intersection of LR market
demand and LR market supply, which is different from
SR market supply.
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8-42
EX1b:c(q)=0.0003q3-0.24q2+70q
LAC=0.0003q2-0.24q+70
LMC=0.0009q2-0. 48q+70
LAC=LMC (so that LAC is at its minimum)
when q=400 (so that LAC=LMC=22)
If QD=21,000-500P. At the LR eq.
QD(P=22)=10,000, one would expect 25
firms to survive the LR eq. to make 0 profit
and Q=10,000.
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8-43
Ex3: c(qi)=40q+0.5qi2
• Suppose every firm has a cost function
c(qi)= 40q+0.5qi2
– Individual supply P=MC=40+qi →qi (P)=P-40
• Suppose there are 50 firms
– QS=50qi=50(P-40)
• If the demand function is QD=4000-10P
– Short-run Eq. →P*=100 (Why?)
– Short-run output and profit? (qi=60? πi=1800?)
• Long-run adjustment?
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8-44
• Long-run eq. of Ex 3:
Suppose n firms survive in the LR eq..When
there’re n firms, QS=n(P-40). The LR eq. will
be p= (40n+4000)/(n+10), q=3600/(n+10)
and Q=(3600n)/(n+10)
Each firm’s profit is 3600(1800)/(n+10)2,
which goes to zero if n goes to infinity.
There’ll be infinity of firms in the LR eq.
• LR eq. price?
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8-45
Challenge Solution
• Increase in the fixed cost of regulatory compliance has four longrun effects:
• Average total cost of a representative trucking company
increases, shifts from AC1 to AC2
• Each trucking company provides a greater amount of service,
q1 to q2
• Market quantity decreases, Q1 to Q2
• The number of trucking companies decreases, n1 to n2
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8-46
Comparative statics for long-run
competitive equilibrium
• Given c’’(q)>0 for n
firms and P’(Q)<0,
at SR eq.,
• If n=8, at SR eq.,
– 𝑃 𝑛𝑞 ∗ − 𝑐 ′ 𝑞 ∗ = 0
• If n=18, at the SR
equilibrium,
• EX2
– 𝑐 𝑞 = 1 + 𝑞2
– 𝑃 𝑄 = 100 − 𝑄
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– 100 − 8𝑞 − 2𝑞 = 0
– → 𝑞 = 10
1.
2.
3.
4.
q=5
q=10
q=15
q=20
8-47
Comparative statics for long-run
competitive equilibrium
• The impact of n on SR eq. (𝑑𝑞 ∗ 𝑑𝑛).
– 𝑃 𝑛𝑞 ∗ − 𝑐 ′ 𝑞 ∗ = 0 must hold for every SR eq.
– 𝑃′ 𝑛𝑞 ∗ 𝑞∗ 𝑑𝑛 + 𝑃′ 𝑛𝑞 ∗ 𝑛𝑑𝑞 ∗ − 𝑐 ′′ 𝑞 ∗ 𝑑𝑞 ∗ = 0
–
𝑑𝑞 ∗
𝑑𝑛
–
𝑑𝑄∗
𝑑𝑃∗
?;
?
𝑑𝑛
𝑑𝑛
=
−𝑃′ 𝑛𝑞 ∗ 𝑞 ∗
𝑃′ 𝑛𝑞 ∗ 𝑛−𝑐 ′′ 𝑞∗
<0
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8-48
Comparative statics for long-run
competitive equilibrium
• The impact of specific tax, 𝑡, on SR eq.
(𝑑𝑞 ∗ 𝑑𝑡).
– 𝑃 𝑛𝑞 ∗ − 𝑐 ′ 𝑞 ∗ − 𝑡 = 0 must hold SR eq. with 𝑡.
𝑑𝑞 ∗
𝑛
𝑑𝑡
–
𝑃′
𝑛𝑞 ∗
–
𝑑𝑞 ∗
𝑑𝑡
=
–
𝑑𝑄∗
𝑑𝑃∗
?;
?
𝑑𝑡
𝑑𝑡
−
𝑐 ′′
𝑑𝑞 ∗
∗
𝑞
𝑑𝑡
1
𝑃′ 𝑛𝑞 ∗ 𝑛−𝑐 ′′ 𝑞∗
−1=0
<0
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8-49
Comparative statics for long-run
competitive equilibrium
• Given c’’(q)>0 for
each firm, P’(Q)<0.
At LR equilibrium,
– 𝑃 𝑛∗ 𝑞 ∗ − 𝑐 ′ 𝑞 ∗ = 0
– 𝑃 𝑛∗ 𝑞 ∗ 𝑞 ∗ − 𝑐 𝑞 ∗ = 0
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• EX2
– 𝑐 𝑞 = 1 + 𝑞2
– 𝑃 𝑄 = 100 − 𝑄
• At the LR eq.,
1.
2.
3.
4.
n=98; q=1
n=90; q=10
n=20; q=15
n=3; q=20
8-50
Comparative statics for long-run
competitive equilibrium
• The impact of specific tax, 𝑡, on LR eq.
(𝑑𝑞 ∗ 𝑑𝑡; 𝑑𝑛∗ 𝑑𝑡).
– 𝑃 𝑛∗ 𝑞 ∗ − 𝑐 ′ 𝑞 ∗ − 𝑡 = 0
– 𝑃 𝑛∗ 𝑞 ∗ 𝑞 ∗ − 𝑐 𝑞 ∗ − 𝑡𝑞 ∗ = 0
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8-51
Comparative statics for long-run
competitive equilibrium
• To see how the small change in quantity tax
$t will impact the long-run eq. dn/dt and
dq/dt, take total differentiation.
– P’n*dq+P’q*dn-c’’dq-dt=0
– P’n*q*dq+Pdq+P’q*2dn-c’dq-tdq-q*dt=0
– P’n*q*dq+P’q*2dn-q*dt=0
é p¢n - c¢¢ p¢q
ê
2
êë p¢nq
p¢q
ùé
dq
/
dt
úê
úûêë dn / dt
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ù é 1 ù
ú=ê
ú
úû êë q úû
8-52
Comparative statics for long-run
competitive equilibrium
• Cramer’s Rule
• For Ax=b, where Det(A) is not zero and x is
a column vector, (x1, x2, …, xn)T.
• xi=Det(Ai)/Det(A) where Ai is A after it’s ith
column is replaced by b
é a b ùé x1 ù é e ù
ú=ê
ú
ê
úê
ë c d ûêë x2 úû êë f úû
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8-53
Comparative statics for long-run
competitive equilibrium
é a b ùé x1 ù é e ù
ú=ê
ú
ê
úê
ë c d ûêë x2 úû êë f úû
x1 =
e
f
b
d
a b
c d
ed - bf
=
ad - bc
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x2 =
a
c
e
f
a b
c d
=
af - ce
ad - bc
8-54
Comparative statics for long-run
competitive equilibrium
dq
=
dt
dn
=
dt
1
p¢q
q
p¢q 2
p¢n - c¢¢
p¢q
p¢nq
p¢q 2
p¢n - c¢¢ 1
p¢nq
q
p¢n - c¢¢
p¢q
p¢nq
p¢q 2
=
0
=0
2
- p¢q c¢¢
-c¢¢q
1
=
=
<0
2
- p¢q c¢¢ p¢q
dp
dn
dq
1
= p¢q + p¢n = p¢q
+ p¢n × 0 =1
dt
dt
dt
p¢q
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8-55